1. With a pastry brush, spread the tablespoon of softened butter evenly over the bottom and sides of an 8-inch springform cake pan.

2. Combine the milk, raisins and ¼ cup of sugar in a heavy 2- to 3-quart saucepan, and bring to a boil over moderate heat, stirring until the sugar dissolves.

3. Stirring constantly, pour the cornmeal into the boiling liquid in a slow, thin stream and continue to stir for 2 or 3 minutes, until the porridge is smooth and thick.

4. Remove the pan from the heat and beat in the 4 tablespoons of butter bits, the rum and the vanilla. Pour the batter into the cake pan, then spread out the batter evenly with a spatula.

5. Refrigerate for a least 2 hours, or until the cake is firm and thoroughly chilled.

CARAMEL SAUCE:

1. About ½ hour before serving, prepare the caramel sauce. In a small saucepan, warm the evaporated milk and the 3 tablespoons of butter over moderate heat, stirring constantly until the butter is completely melted and small bubbles appear around the edge of the pan. Set aside off the heat.

2. In a heavy 1- to 1½ -quart saucepan, bring 1 cup of sugar and the ¼ cup of water to a boil over high heat, stirring until the sugar dissolves.

3. Stir in the cream of tartar and boil the syrup briskly over moderate heat, gently tipping the pan back and forth almost constantly, until the syrup turns a deep golden brown.

4. Then pour in the hot milk mixture in a thin stream, stirring constantly with a large spoon until the caramel has thoroughly dissolved. Remove the pan from the heat.

5. To serve the "gateau mais", remove the sides of the cake pan. Run a long metal spatula under the cake and carefully slide it onto a large platter.

6. Serve the caramel sauce separately in a small bowl or sauceboat either warm or at room temperature.